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Anomalous Hall effect and rich magnetic phase diagram of Mn$_{100-x}$Rh$_{x}$ epitaxial films

A series of Mn$_{100-x}$Rh$_x$ ($20 \le x \le 50$) thin films were epitaxially grown on the MgO substrate using magnetron sputtering technique, and were systematically investigated by magnetization, longitudinal electrical resistivity, and transverse Hall resistivity. After optimizing the growth conditions, phase-pure Mn$_{100-x}$Rh$_x$ films with a cubic CsCl-type structure were obtained, and their magnetic phase diagram was built. The manipulation of Rh content leads to a rich magnetic phase diagram, where three different regimes can be identified: for $x < 40$, Mn$_{100-x}$Rh$_x$ films undergo a ferromagnetic (FM) transition below $T_\mathrm{C} \approx$ 330-350 K; for $40 \le x \le 45$, in addition to the FM transition at $T_\mathrm{C} \approx$ 200 K, Mn$_{100-x}$Rh$_x$ films undergo a FM-to-antiferromagnetic (AFM) transition at $T_\mathrm{N} \approx$ 120 K; finally for $x > 45$, only one AFM transition at $T_\mathrm{N} \approx$ 150 K can be tracked. All the Mn$_{100-x}$Rh$_x$ films exhibit distinct anomalous Hall effect in their magnetically ordered state, which is most likely due to the intrinsic Berry-curvature mechanism. In addition, all the anomalous Hall transport properties, including the resistivity, conductivity, and angle exhibit a strong correlation with the magnetic properties of Mn$_{100-x}$Rh$_x$ films, which become most evident for $x$ = 35. Our systematic investigations suggest a strong correlation between magnetic properties and electronic band topology in Mn$_{100-x}$Rh$_x$ films, highlighting their great potential for AFM spintronics.